Arthur w



A. W. MACMILLAN.

CALCULATING DEVICE.

APPucAnoN mso rfa. 6. 1915.

Patented Aug. 22, 1916.

2 SHEETS-SHEET l.

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f ATTORNEYS. I? @59W A. W. MACMILLAN.

CALCULAHNG DEVICE.

APPLICATION. FILED FEB. 6, 1915.

1,1 95,702. latlltmi Aug. 22, 1916.

2 SHEETS-SHEET 2.

vWEATHER SUBJECT IO 24 hun /Jfm WJMMLWM A TTRNE Y UTED sTATEs Ba'iiin'r OFFICE.

ARTHUR V. MACMXLLAN, OF CHICAG. ILLINOIS. ASSIGNOR OF ONE-HALF TO ALBE H. GRAVES. OF CHICAGO. ILLINOIS.

CALCULATING DEVICE.

Specification of Letters Patent.

Patented A ug. 22. 1916.

To nl] /r/Lom. it m (1 1/ #0n/'cr l lie it known that I. Aurnin ll". MACMIL- i..-\.\'. a citizen of the I'nited States. residing in Chicago, in the county of Cook and State 5 of Illinois, have invented certain new and useful Improvements in Calculating Devices, of which the following is a specification.

This invention relates to .improvements in calculating devices, and refers more partic ularly to a device for rapidly and accurately determining, wit-hout the. use of involved arithmetic-al computations, the value of a quantity`which is the result of the combined effect of'several variable conditions or circumstances modifying the subject-inatter of the calculation.

Although the invention is capable of many modifications for different uses, yet I have found it to be of particular service in con- .nection with photography. Hence, I will describe, as a specific application of the invention, a device for rapidly and accurately determining the correct exposure period for 'photographic platesor films when exposed under' any stated chronological,` weather, subject, and instrument, conditions.

The specific embodiment which'I have se- `lected as illustrating the application ofv my invention contemplates the provision of a graphic exl-)osiire-chart in which the several more important variables which enter into the conditions controlling the proper time of exposure may be `readily taken into account and due allowance made therefor.

with accuracy and despatch; a chart of such form and simplicity thatA a chart sheet may be used, if desired, for each exposure and a "graphic record `of the determinations made and preserved; a form of chart which wholly-l dispenses withve'very kind of arithmetical calculation and-fresolves itself simply into the tracing of lines, yettakes into account all of the important variables in making the deductions; a chart in which is disclosed an underlying principle of construction and arrangement. enabling it to be inade for any' given Zone or latitude in the. world; and, in

general, an --improved calculating device of the character referred to.l

To the above ends thel invention consists' m the matters hereinafter described and more particularly pointed outin the appended claims.. h r

Figurejl snows my invention embodied The principles of my invention will be.

readily understood by reference to Fig. 1 and the following description. In said figure. the short horizont-a1 line at the top of the figure represents an initial base line or .datum level from which are measured or set off (as ordinates) the starting or predetermined value of' the'quantity which is subject to varying conditions and whose value as affected or modified by said varying conditions is to be graphically calculated. In the present case the level or height of` the first initial base line represents a certain exposure period. according to standard condi tions of calendar, hour of. the day, light value, kind` of picture and stop opening with a standard-speed of photographic plate. The standards which I prefer to adopt are maximum values in each case in order to simplify the chart.

VThe ordinateE represents, according to a predetermined logarithmic or geometric scale, a certain; increase of' =exposure time necessary for a given. time of the year and hour of' the day. That is to say, the points located between the lower end of the ordinate E and the first base line will represent factors, arranged in a regular geometrical progression, for multiplying theoriginal or standard exposure period, the va'he of which is represented by the first base line. In the upper right hand corner of the figure I lay off a set of oblique lines l1, l2, Z3, l* which represent light values corresponding to different atmospheric conditions, the first oblique line Z1 representing an atmospheric condition which has a maximum light value, and the other oblique lines Z2, l and l* representing certain atmospheric conditions having lower lightvalues. These o'blique lines Z1, l, Z3 l* are spaced apart according to their multiplying effect upon the origina-l standard or 'maximum atmospheric light condition and are arranged in a geometrical progression. For instance, if

the. condition Z2 require double the exposure of the condition Z1, the line Z3, which', in the present case, is spaced apart from the line Z1" twice as far as the spacing between the lines 65 have used the Z1 and Z2, would represent an atmospheric condition requiring four times as long an exposure as would the Ycondition Z1. Similai-ly, the oblique line Z4 would represent an '5 atmospheric condition requiring eight times as long an exposure as the originalcondition Z1, assuming of course that the lines Z1, Z2, Z, Z* -wereequally' spaced apart. It is Anot essential lthat the inclination of the oblique parallel lines Z1, Z2, Z3, Z1 should be at any definite angle to the first base line. However, for convenience, I employ an angle of 45, which enables me to plot iiiy geometrical logarithmic values all to thel same scale, the sine and cosine of said angle being equal, thereby making the preparation and l use of the chart as simple as possible.

At the intersection ofthe firstwbase line with the oblique line Z1 there 'is awnthe ,second base line, which, in this casefis found 4to b e at right angles to the first base line. 'e are now ready 'to calculate graphically the length of exposure E as modified by one of the inferior atmosphericconditions, Z2, Z, or Z1. In the present instance we select Z2. At the lower end of the ordinate. E I simply draw a line, which, for convenience, I call a first guide line "parallel tothe first base line, andF which intersects the oblique line Z' thus giving me I call E l2. between the points` of intersec` tion of said first guide line with the second base line and the oblique line Z2. Measurement of the distance E Z2 in comparison with a predetermined geometricscale simi- '.lar in character to the geometric scale to which is plotted initial exposure value E,

willl give the proper exposure value of the Yoriginal exposure period E when subjected 40`to the inferior atmospheric condition Z2. It should be understood that the spacing of the lines I1, Z2. I, Zt is measured in a direction which is parallel to the 4first base line,

'since the first guide line is always drawn parallel to said first Abase line,` irrespective `of the inclination of said oblique lines Z1, 2, l, Z, orv ofV the angle which the second base line makes with the first base line.- It should also be noted that the spacing apart of the lines Z1, Z2, I, Z, measured in a direction parallel to the first base line, is-always A proportionate to the angle made by the second base line with the base lines Z1, Z2, 3, 1; so that whatever the initialstartingvalue may be and at whatever distance the first guide linev may be-drawn from the first base line, the second ond base line and the points of intersection of the first guide 'line withvthe oblique lines Z1, Z2, Z3, Z1, will always be inv accord with the' geometric values representing the distances apart of said oblique lines. However, since I have adopted an angle of 45 and the distance, which` geometric scale, by which; are measured the distances between thesecsaine geometric scale fcrthe initial values E and for theV atmospheric values Z1, Z2, Z3, Z, I am enabled to for measuring off' the corrected value E Z2 the same geometric scale which is used to lay ofi' the initial valueE. In this respect the vscales which I employ are similar to those found on the ordinary slide rule for dividing or multiplying numerical quantities.

Now that the principle ofthe invention has been disclosed, I will explain how I extend' its application so as to take care of more than one variable condition to which the initial predetermined value is subjected` For instance, in the diagrammatic embodiment of the invention which I am describing as applied to determining exposure values for photographic purposes, it is possible to take into account every variable condition which is encountered in photography. However, in order to simplify the description, the variables representing differences in con'- ditionsof picture values and stop values are the only additional variables which I shall describe here. In the diagram, Fig. l, it will be observed that at the lower side of the second base line I have drawn au oblique employ line p1 also at. 45C to the secondoaseline and representing a subject or picture which requires the minimum exposure period, the oblique lines p2, p3, p1 representing the subjects or pictures of lower light emanating quality, which require progressively loiiger exposures than in the case of the standardor maximum subject or picture represented by p1. At the intersection of the second base line is at right angles to the second base line. It is of course understood that the spaciiigs of the lines p1, p2, p3, 7)", measured in a direction parallel to the second base line, represent, plotted according to a geometric scale, factors for multiplying the unmodified or with ,the line p1 I draw a third base line which Istandard exposure values. The second guide line is drawn parallel with the second 'base line from the intersection of the first guide line with the atmospheric light value line Z2 -and is extended downwardly unt-il it intercorrespoiids to the parsects the line which ticular kind of picture which it is desired to photograph. In the present case we will assume that. this is the line p3. The perpen-V dicular distance E Z2 p3 measured from the third baseline to intersection of the secondguide line of line p3 then represents, according .to the proper geometric scale, a length of exposure which is the original exposure vvalue E as modified by the atmospheric conditions AZ2 and picture value condition p3..

In a similar manner I am enabled to allow I for various stop values. the left hand of the third base line I may draw another set of oblique lines s1, s2, s3, s* representing various stop values, and at the intersection of tliethird base line with the stop value. representing a standard or maxi- For example, at

nimmer i ha l p/frpemlicizlzir i th: third hase and at in angle of Ti lo the ohliiiue linee. 'llw lnir-.l guide line drawn lion oi' thc Second Aguide -i w with ilu picture value line if' and is del to the third, ieri line o :la to ie oliiioue stop vaina linea; lil it t; lo calculate a length of exposiure u'i a #top lo he mcd. the third line ro'ltinued until it :morsi-liv the recaiitant cillin re wriol iq in Said inicisi'fiion ifi the i c fvcuwlingloiuinropcr ,':intd li",y u il v lit is in? nisirl ml the @auw nld he extended in order 'to coinvarious types of platee or films i, Spoedig or for any other farb itionf: which might oc encountered,

i .ltliougl l' have descrilicd my invention lird to :V-,aloulating exposure periods, d la; iiinfiierstood that thc invention is 'mnt number of applications; uit it i' lie found of value wherever nwzwwary 'io calculate the modifying ons iu more varialile conditions. l row deocrihe the exposure cham'J n. which illustrates :i practiin of my invention to thc com nl ufiliez the principles described.

m with Fig, l.,

device or guide embodying lf; developed on tho principle moet intr-noe iight of that v and giver when light iS ing; a photof'raph ot" the suh- H si lightmreflecting value and the iporurie wade with the largest stop, will redo' e a minimun: period of exposure, and :naiv ihffrc'oro represent' one end of a scale, cnil of which avale is determined weft light "allient the Sum of the entering into an exposure inout adverse conditions. e., llgzh values which are to be l was nich dan it will neem, upon @tor` that all the variables: dealt cepi'oeei'u, ini'rrinfzntn of time in the i time lli/:tvforen luf-canne .'uf'h variae cach and all of .-s light value than winmiu liv plattingz the scveral varin il on the uw alc. allowances in nrcfcmieil ivy diamine, and lu' them toe'chcr and referring dirimir# to the final expo o coursin plotted on .H4-alc) lw corrected fi-n Sci ol' conilitionz# Yillu iihul elle Alli rlopoi'ion lo thc nvtual ill civoosurv period hut will lio prcivralillv u gfemnctrical scale so that iivrenients oli (n ik i rio mm1 creased time of exposure due to icngih of the Several variables when added touchcr haw a multiplying effect on, the initial value of exposure period.

The 'foregoing principlesI of construction and :irrangemcnt will lic netter understood from :i description of the illustrated chart ehoo'n in Fig. 2, which embodies one examplc. thereof. (ln suitable coordinati paper, l develop a group of curves orgraduations for :he diii'crrnt timex of year. each such curve reprcseuting a period during which the iight of approximately equal value, ani?x all ol' the curves being properlj,y Cordinuwl with :i scale of hours of' thc day. In llo: chart lm, group of time curves is assofiicd nifl the word "Month". and they are rlwrrall'Y designated hy the months to which they pertainn The hour Wale referred to is arranged along the axis of ordinates4 Common to their time curves. and designated (1,. 'The distance or length of ordinate from any point on the axis` of ordinates` r1 to a point of intersection on a given month curve co1`A responds to the length of timer exposure for the. time .so coordinated. J

To the right, and horizontally opposite the group of month rurvcs is provided a group of weather curves or graduatioml un der the healf ing Weatheg these curves heing arranged nt an angle of with ref erence to the squares of the paper, and inasmuch are they represent more` or less arbitrary grasluatious of the weather Variables. they arey marl? rstraight and parallel. lt will hc noted that, reading from left to right, tlm` irst grmlnation-"Bright sun"-repre sientes tho highest light value. and each sue weeding graduation a lower light value, to 'the lowest-Mthat designated Very dull. The projected distances between these wearhervariahle graduations represent the allowances (in length) on the scale for inthe existence of such variables. Hence, the projected distance from the curve designate( Bri fht sun" to the curve designated Very dull would reprenant the allowance for an exposurc time on a very dull day, while if auch exposures were made with lli-ight sun no allowance would he made for weather variable.

vertically below and opposite the group of weather curves iS another group of such curves or graduation; designated as a group Sl\h iect". and which curves are severally marked with proper lcgends. Here again the uppermost curve, or that nearest the weather curves, represents the highest light valuef und the lowcrniot the lowest light value. and. so also. the vertical Spacing lwtucen curves rvprcnenta in distance the allowances for the Several variahlcs iueasur ing downward Jfrom the lirst curve Studies ol' white clouds as zero.

To the left, und horizontally opposite the subject eurves. is arranged a froup of tt eurves. designated Stops", 'l lee :stop eurie to he extreme right represents the smallest `top used in prartire. viz.. the F il or i7. H. 1::y .topi and the sneu-ssi ve stop curves from right to left are platted to roi-respond ith the usual graduation ot' stops. llenee` treat ing the curve l*` i as unity, the distanre from left to right arrose; the entire series of stop eurves lnnixontallv will represent the maximum allowanre to be made when usine the smallest stope l llireetly below the group of stop varie and extending along the axis oi' ordinates f3 ot' this group of wirres. is the final e\ posure scale laid out in units of time. and designated "Seronds exposures". 1n tin` ei;- ample given. this srale follows the graduations eommonly adopted b v American eani eras. from .uol seeond to one full minute, and while these values a 3 approximatelwiY on the geometrirai progression of Zini. still the graduation marks are not exaet. hul represent eonvenientlv approximated fractions.

The hart desi'ribed niahv be used either by tracing the sueeessive alion'anees through with the eve. b v the aid of the vertical and horizontal lines. or ma)v be more aeeuratelv and reliably traeed by drawing a continuous peneil line from one variable to another, and finally to the exposure srale, thus not only enabling the artist to verify his traeing, but giving him a reeord whieh lie may permanently preserve if he so desire'. To illustrate.l suppose it be desired to malte an exposure at haltl past eight or half past foar on a da)v in lune or July, the 'weather being dull. the subjeet an average landscape. and stop selected No. 163. The artist will start from the star` designated r' in the drawing, trace the ordinate to its intersection with the June and July eurve` then turn at right angles along the line n' to the point of intersertion with the curve marked Dull, at that point turn at right angles and trace downwardly alongr the dotted line designated e to an interseetion with the eurve marked Average landscape, then at right-angles alonlgr the dotted line f to a. point of intersection with the step line 16, and then projeet at rigbbangles down wardly to an intersertion with the seeonds exposure scale. This will show that the proper exposure for the Conditions referred to should be about 2 of a second, but the ramera shutter would need to be set at the l second. as being the nearest approximation to this correct time.

It will be seen upon consideration that this chart; as devised, enables the operator to cumulate the proper allowances and pro-` jert the sum of these'allmvanees apross the seale in a purely ineehameal out caluiatwn. This feature is in itself an way, e., Withmesyoz important eharaeteristie of this bodiinent of the invention.

Explaining: how the operation of the Scale may be verified, it will be understood that inasmueh as the aetuai foot of the seule shown startsv .vith a .util exposure.thedatum point of the rale wpuld he ronsiderably below or to the left of the .Olli graduation marit. lts theoretiral loratiou is indif'fited in dotted lines` at f1 ,uni this point is dw teruunal bj, evt-inline the axis ot' ordinates ofl the month rieur unid it int-:nrierts The ti"-:t of the weati -r am". thenee eontinun uit: at rightaxngfies :unil the line intersects `he tirs-t ot' the subjert eurvesl and then at rightaingjies horizontally to the left to a point whirh iuterseets the continuation of the largest atop wurm; j". and finali)Y at rightaugles downmirdl;v to a point of interseetion with the seale iine g.

To verify the determining of the set of eonditioiu: above trarwl as an example. the following: ailowanre:` are eumulated., and this may be rradilv done with a pair of dividere: "from star .fto interseetion with Jane and July" eurve: from curve Bright sun` to eurve "l)ull": from curve lVhite clouds" to eurve Average landscape; from stop eurve f* or l to stop curve 16. These distantes riuuulated will represent the distanee between the theoretiealtfoot of the seale designated and the Correct ex posare time. designated .5.

t will be observed that in the practical embodiment shown in Figi L. the only' Shale shown i.-- the iinal scale. by which I take olf the final eorreeted values for the time of eX- posnre as modified bv the different variables. Inasmueh as :he final seaie is the only one whit-li need be used for this purpose, it is unneeessar)v to provide intermediate scales .for the other parts of the ehart. Similarly. it is unnecessary actually to draw on the commercial chart the various base lines used in laying out the time enrves or the oblique variable lines. lVhen laying out the chart initially it is of course neeessary to estahlish -virtual base lines from which to set. out the various curves and lines, although these may' not be shown in the printed Chart which is furnished to the photographer. As a matter of fact, the guide lines are eoordinate lines in etlect, or base lines.

The month curves cordinated with time of day have been platted with approximate correctness from ascertained data for a latitude. corresponding to Chicago. It-will be observed that the curves representing exposure values tit-different hours for the varions months are not parallel with each other, nor are they straight, but drop of! abruptly at their right-hand ends. This is because in the winter or early spring months at certain hours of the day the light values speeifie ein` rangement,

change much more rapidriv than in tht` middle part of the dav. Ilence. thel use of graphic. curves for the inltial exposure values is particularly :nlvautageons and is far more. reliable and accurate than a table. The weathercurves and the subject curves represent estimates in the classification of the allowances, and, as shown. have been uniformly spaced apart. These spacings may be. changed` if practicalaml widely extended use ofthe chart indicates abetter spacing. i. c., a spacing which more correctl coincides with the average judgment of the users in determining theseweather and subject conditions` AThe stop curves have been spaced willi approximate correctness to correspond with the sizes of ops which have been generally adopted in photography.

lt will, of course', be understood, now that principles of the invention have been explained` thattbe invention may be em-V bodied in forms different from the particularehart herein shown.

In actual practice the chart is printed on inexpensive sheets of paper and a multi plicity of sheets bound into :i tablet, so tha-t the artist may make. his exposure record. and such other data as he chooses, on the sheet` and then ren'iovcthe sheet. from the tablet for preservation; thus. using la new sheet tor each exposure.

-In the matter of simplicity of use. com'- paetness of forms, and simplicity ofrarthe -.particnlar embodiment herein shown has special advantages of its own', which are made the'subject of specific claims. The makingT of specific claims is not to be, understoodl las implying that the.

f broader-claims are to be construed 'as relating to this specific type of'wthe invention.

l. A calculating device, comprising a sheet having marked-Ona portion of its aveaa`curve,V the ordinates of which represent predetermined -valnes of a quantitygzi set of guide-lines extending from said area and 'making an anglel with said ordinates, a set of oblique,` parallel cross-lines intersecting said guide-lines at an angle, said crossdines lxzingspaced apart proportionate to thev modifying effects of .predetermined values' of a variable which' theyiepresent, and a third vset of parallel guide-lines intersecting said first twb sets of lines and spaced apart proportionate to the differences between the values of the corrected resultant quantity to be determined, the positions of said last-named lines, When referred to a suitable common scale,-representing, as modified by said variable, corrected values of thel original predetermined quantity.

2.V A device for ,multiplying predetermined values of a quantity with different values ot'a variable quantity, comprising a ing efi'ect of .tlre variable and according to.

a geometric scale. and -a set of parallel guide-lines at right angles to the first setintersecting said first ltwo sets of lines and spaced apart.proportionate to lthe (litter`- ences between the corrected values of the*v multiplied original quantity, the distances of said last-named lilies from a baseline at right angles to said first base lille, when referred to a suitable geometric scale. represeuting` as modified by said variable, the product of' the original quantities as multiplied b v said variable.

graphic calculating device for determining thc modifying effect of a variable upon'au original predetermined quantity. comprising a sheet having inscribed-on its f'ace a set of oblique, parallel lines, spaced apart prolmrtionate to the predetermined modifying effects on said original quantity of difftirent values o f a variable condition represented by said lines; increments of spacing representing increments of modifying effect. said oblique. lincsbeing suitably arranged to -be intersccted'lja guideline drawn parallel to an initial virtnal'base line and at a distance therefrom proportionate to a predet-ermined;value of .the initial nnmoditied quantity. incremeiifs of said distance representiiig increments in value of said quautit)y actiirding to au initial scale, the listances of theA points of intersection `of'isaid guide-line with the oblique. lines of said variable represented b v' said oblique lines.

termining the modifvii'ig effect of two variables. upon an original quantity,l comprising a sheet having inscribed on its face'a set, of oblique. parallel lines, spaced apart proportionate to the predetermined modifying eft'ects on said origi nal quantityt of different Avalues of a variableI condition represented by said lines, increments of spacing representing increments of modifying effect, said oblique .lines being suitably arranged to be interseeted by a guide-line drawn parallel to auinitial virtual base line and ata distance therefrom proportionate to a predetermined L graphic.*calculating dcvicc.- for de-' predetermined iis the oblique linesfrom a second'virtual baseline, making angles with said oblique lines,

representing partially corrected values of -said originalfquantity, a second set of oblique parallel cross lines, analogous in character and function to said first setA and.- representing values of a second variable and arranged to be intersected by a guide-line drawn parallel to said Second baseline from one of said intersections, lthe distances of the points of intersection of said second guide-line froma third virtual baseline making angles with: said second guide-line and said second set of oblique lines, representing, when referred to a suitable scale inally corrected values of said original quantity as modified by the variables represented by said sets of oblique lines.

5. A chart for determining the effect of a predetermined variable light condition upon a predetermined standard exposure period, comprising a chart having marked on a portion of its area points, ordinates to which romfa 'virtual base line represent standard exposure periods at differenty times under various calendar conditions, the values of said ordinates being plotted to va suitable geometric scale whereby increments in length represent multiplying factors, a set of parallel guide-lines crossing said area parallel to said base line, a set of parallel oblique cross-lines intersecting said guide-lines and spaced apart proportionate to-the multiplying effect of different values of a variable light condition represented by said crosslines, va second set of parallel-guide-lines intersecting said first two sets of lines and Vspaced apart proportionate to a suitable geometric scale, increments of spacing of which represent incrementsof multiplyingr power, a second set of oblique parallel crosslines analogous in character and function to said first set and representing values of a second variable light condition, guide-lines intersecting said gross-lines and said second set of guide-lines, .the spacings of which also represent multiplyinfr factors plotted to a .geometric scale, a thirdset of parallel oblique cross-lines intersecting said last named guide-lines and representing,r stop values, and a final scale representing finally corrected exposure periods plotted to a. suitable geometric scale and connected by guidelines to said last named set of parallel oblique crosslines. I

6. A graphic'calculating device, comprising a sheet of paper having inscribed upon itsv surface a curve, the ordinates of which represent predetermined values of an initial quantity, the actual va'lue of which when it is modifiedrby a variable 'condition is to be determined, the points on said' curve being plotted to a scale the graduations of which represent values of a geometric progression, a set of oblique cross lines adapted to be intersected by perpendiculars drawn from said ordinates toward said oblique cross lines, said oblique cross lilies representing different values of the variable condition 'and spaced apart in lthe direction of said perpendiculaire, according to a scale the e ual graduations of which represent values o a geometric progression, increments .of spacing of said o lique cross lines representing multiplying factors, the distances of-the points of intersection of said perpendicular-s with said oblique linesfrompapredetermined virtual base line representing, when referred to the same geometric scale -by.

which said oblique cross lines are spaced, the

values of the initial quantity as modified byv y said variable condition.

7. A chart for graphically determining exposurefvalues, comprising a fiat sheet having inscribed u`pon its surface ,a set of curves each representing a calendar condition, the

ordinates from a virtual base line ofpoints on each of; said curves representing llogarxthms, the antilogs of 'which represent factors for multiplying a standard exposurey period' at partil'sularhours of the day, a set of oblique cross-lines `adapted to beinter-l sected by guide lines perpendicular to said ordinates, said oblique cross lines being spaced apart in the direction of said pendiculars accordingto values of og;

'arithms of quantities representing-the multiplying effects of different values of the variable condition represented by the positionsv of Vsaid oblique cross lines, said latter named logarithmic values being measured from a second virtual base line, a second set of oblique' cross lines, spaced apart yin a similar manner,I representingl different conditions of the second variable' and arranged to be insaid last named base line fromv the intersections of the first guide lines withthe first set of cross lines, a third .virtual base line similarly arranged in connection with said second guide lines, a third setof oblique cross lines representing values of a third variable,

spaced apart in a similar .mannen and adapted to be intersectcd by guide lines drawn parallel with ,said third base line from the intersections with the second obric-progression according to a logarithmic'v tcrsected by guide li'nes'drawn parallel to L scale, said scale beng adaptuu' to be inter sccted by limes drawn parallel with smid fourth base line and from the interscctuns of the third guide lines with Said third. sei; of oblique cross lines, the pxwtons Uf said iirst, su'ond, third und fourth base line` rey resuming u time of exposure under standard conditions of all 0f the vnrinbhes dffait with in the chart.

ARTHUR YV. MAGMHAN.

Witnesses C. A. SQANS, Ennuh: ROSE. 

